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I. Reduction Technique

With the atomic clocks and VLBI catalogues of extragalactic sources, the theory-independent references for both space and time will be quasi ideal in their underlying principles (non-rotation of very distant objects, constancy of the frequencies associated to atomic transitions). The paper is an attempt to clarify the role of these natural references with respect to those which are implicitly defined by the dynamical theories.

The example of time is discussed, since it already gave rise to serious difficulties, but similar problems may occur about the space references. Such complexities are suprising: one could have expected simplifications from the use of references which are not entangled with theory. Some suggestions are made for the use of these natural references.

The new definition of UT1 adopted by the IAU is useful but for many reasons not quite satisfactory. It depends e. g., 1) on the approximate values of some astronomical constants, and is therefore subject to revision in the future. 2) Since it is used for the FK5-based astronomical reference system, its eventual usefulness for space techniques is questioned. 3) Although the new and old UT1 merge continuously at a chosen epoch, they do not form a homogeneous series of data, in other words, the old and the new UT1 are systematically different from each other. 4) Neither the new definition, nor the way to convert the old to the new one is based on simple concepts and these are thus likely to be misunderstood by the nonspecialist user. A conceptual definition of UT1 is suggested, in order to correct this situation and a formula to realize this conceptual definition is presented, which can be used unchanged for every technique and is easily understood by the nonspecialist community.

The nonuniqueness of the quasi-Galilean coordinates of general relativity leads to the emergence of unmeasurable coordinate-dependent quantities in astronomical practice. One may offer three possible ways to overcome the related difficulties:
1.

developing theoretical conclusions only in terms of measurable quantities

2.

using arbitrary coordinates and developing an unambiguous procedure for comparing measurable and calculated quantities

3.

agreement to utilize one and only one coordinate system.

In this paper we prefer the second way. After formulating the heliocentric planetary and geocentric satellite equations of motion, the general technique for relativistic reduction in astrometry and geodynamics is developed. Specific algorithms for the reduction of absolute and relative measurements are derived for the one- and the two- body problem. For illustration, the relativistic reduction of stellar parallaxes, Doppler satellite observations, navigation measurements with the aid of satellites and radiointerferometric measurements are presented in detail.

Proper motion surveys offer a great deal of data bearing on important astronomical problems such as stellar kinematics and the luminosity function in the solar neighborhood. Major obstacles to the full use of proper motions have long been posed by: (1) incompleteness of proper motion surveys, (2) proper motion bias in kinematic studies, and (3) the indirect approaches and kinematical assumptions needed in traditional luminosity studies.

The importance of understanding the properties of a data sample which is to be used for calibrating luminosities can hardly be overemphasized. In an earlier paper (Lutz 1983) I pointed out the methods for dealing with two well-defined cases. In this paper I will elaborate further on the same topic.

An investigation of the N30 along the same lines as that of the FK4 (Brosche and Schwan 1981) reveals quite similar non-standard systematic motions. Some consequences are indicated for the determination of cluster parallaxes, of secular parallaxes and of the galactic rotation. In general, we stress the necessity of always searching for every signal in the data - including those ones which are not understood and hence not ‘wanted’.

A survey of the various tasks involved in the construction of the Fifth Fundamental Catalogue (FK5) is given. One of these tasks is the determination of the FK5 system which will be performed with the aid of new analytical methods developed at Heidelberg. The basic characteristics of these methods are described, and information on the most significant errors in the FK4 system is given.

Currently the computation of mean positions and proper motions for the International Reference Stars (IRS) is hampered by large variations in the observational histories of the stars and lack of overlap between the magnitudes of the IRS and of the FK4. The poorest IRS observational histories are +60° to +80° in the north and −40° to −80° in the south. The much-needed extension of the fundamental system to the ninth magnitude will be made in the FK5. The Faint Fundamental Extension is currently being selected at the U. S. Naval Observatory. A proposed list of 1030 Faint Fundamental stars has been prepared for the Northern Hemisphere, and work has begun on the selection in the Southern Hemisphere.

A variant of Brosche's well-known method is proposed which allows one to represent systematic differences (many times faster than with the original method) by the use spherical harmonics. The improved economy of computer memory requirements and reduction of calculating time are achieved by replacing the two-arguments approximation with a sequence of one-argument approximations, and by enforcing an equidistant distribution of the initial differences along the α and the δ directions. The proposed method was tested on models and used for representing the systematic corrections Δ δα and Δ μα to the catalogues GC and N30.

Fundamental meridian circle observations require the variation of latitude to be applied before the observations are combined to form a catalogue. In the past 80 years, different observatories have used various determinations of polar motion to reduce their observations. This study shows that the use of different determinations of the latitude variation significantly affects the individual observations and can introduce large zonal errors of the level of 0.05 seconds of arc into the catalogue's declination system.

Fundamental observational programs are often lengthened because of the sparsity of data during bad weather seasons and the need of having strong links all over the 24h of right ascension. The global reduction procedure tries to minimize this problem by making more efficient use of the available information with full consideration of incomplete or isolated group observations. The whole set of observational material is treated as a single least squares problem, whose unknowns include corrections to the star positions. The problem is usually of huge dimensions, but we show that it can be reduced to quite tractable sizes. As an example, the method is applied to a two year series of astrolabe observations. The time and latitude curves are solved for under the form of cubic spline functions. The results are equivalent to those of conventional procedures, provided due account is given to the fact that, in the global reduction, long period components of image motion are fully included in the standard error estimates.

The most usual method for the determination of the angular separation ρ and the magnitude difference Δm of the two components is the direct comparison of the observed diffraction pattern with a theoretical model. However, it is possible to use a deconvolution process based, for a single star, on the equation I′(x) = F′(x) * O(x), involving both the derivative of the Fresnel diffraction function for a point-like source, and that of the observed intensity. O(x) is the brightness distribution function of the occulted source.

We describe here a new method, using the integrated deconvolution process (Froeschlá, Meyer, 1983), in which we determine the variations of the apparent surface of the two sources of a double star while it is being occulted. The two sources are supposed to be of the same diameter. This method has been applied to several cases of theoretical diffraction curves with different values of ρ and Δm. Noise has been added and we have studied the effect of the signal to noise ratio on determination of the parameters ρ and Δm of the pair. A good accuracy for Δm is obtained for |Δm| ≦ 1 and noise ≦ 10%. The determination of ρ is well achieved for noise level reaching 15 %. The technique has been at last applied to the observation of the occultation of SAO 95166 made by Africano et al.(1977) leading to nearly similar results.

We present here the fundamental idea of the conversion method between old and new reference frameworks. Some practical applications are made for the optical observations for Tokyo PZT. The method can be also applied to the conversion of radio sources where we have met a great difficulty in performing the conversion because of no citation of observation epochs in general. We discuss their necessity in order to establish a concrete compilation of the position of the radio sources.

The fundamental reference of the Earth rotation observation by the method of optical astrometry, such as VZT, PZT, astrolabe, transit instrument and so on, relies upon the stellar system. Hence the stellar positions and proper motions, and the celestial reference coordinate system are essential to preserve the system of the Earth orientation parameters determined by the optical astrometry.

In the application of Very-Long-Baseline Interferometry (VLBI) to astrometric problems the fundamental observable is the difference in the arrival times of a wavefront at two widely separated receiving stations. Since the radio sources being observed are sufficiently distant that the arriving wavefront can be considered to be a plane wave, the differential arrival time is a measure of the component of the baseline in the direction of the source. Equivalently, if the baseline is known, the differential arrival time is sufficient to determine a circle on the sky containing the source. It is easy to show that a minimum of ten observations distributed among three different sources is sufficient to determine all of the source coordinates and the baseline coordinates simultaneously (Robertson, 1975).

A celestial coordinate frame defined by extragalactic radio sources has been developed from Mark III VLBI data. 33 000 delay and delay rate pairs acquired between August 1979 and December 1982 have been analyzed to give positions for 82 radio sources. Standard J2000.0 astronomical models were applied. 90% of the formal errors for arc lengths between sources are less than Arc lengths estimated from separate one-year data sets are consistent at the to level.